A path of length n is defined as a sequence of length n of increments.
Let L be the last maximum and \nu the number of steps ending above zero.
 
We define a bijection \sigma on paths that maps a path, \gamma, 
of length n to a path \gamma' of length n by permuting the steps 
(so S_n remains the same and the measure is preserved) such that 

	\nu(\gamma) = L(\gamma').  

Define \gamma' = \gamma if n = 1.  If n > 1 and S_n <= 0 then
decompose \gamma into (\gamma|_{n-1} , X_n) and define 

	\gamma' := ((\gamma|_{n-1})' , X_n).  

If n > 1 and S_n > 0 then define 

	\gamma' := (X_n , (\gamma|_{n-1})')

To see that this works, use induction, the verification being
trivial for n=1.  Assume n > 1.  If S_n <= 0, then L(\gamma)
= L(\gamma|_{n-1}) and \nu(\gamma) = \nu(\gamma|_{n-1}) so induction 
hypotheses implies L(\gamma') = \nu(\gamma').  If S_n > 0 then 

	\nu(\gamma) 	= 1 + \nu(\gamma|_{n-1})
			= 1 + L((\gamma|_{n-1})') 
			= L(X_n , (\gamma|_{n-1})') 

as long as the first max of (X_n , (\gamma|_{n-1})') does not occur
at 0.  This is guaranteed by S_n > 0 and we are done.